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Multinomial Level-Set Framework for Multi-region Image Segmentation

  • Tammy Riklin Raviv
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)

Abstract

We present a simple and elegant level-set framework for multi-region image segmentation. The key idea is based on replacing the traditional regularized Heaviside function with the multinomial logistic regression function, commonly known as Softmax. Segmentation is addressed by solving an optimization problem which considers the image intensities likelihood, a regularizer, based on boundary smoothness, and a pairwise region interactive term, which is naturally derived from the proposed formulation. We demonstrate our method on challenging multi-modal segmentation of MRI scans (4D) of brain tumor patients. Promising results are obtained for image partition into the different healthy brain tissues and the malignant regions.

Keywords

Multinomial Logistic Regression Brain Tumor Patient Tumor Segmentation Healthy Brain Tissue Dice Score 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)zbMATHGoogle Scholar
  2. 2.
    Brox, T., Weickert, J.: Level set segmentation with multiple regions. IEEE Trans. Image Process. 15(10), 3213–3218 (2006)CrossRefGoogle Scholar
  3. 3.
    Chan, T., Vese, L.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dempster, A., Laird, N., Rubin, D.: Maximal likelihood form incomplete data via the EM algorithm. Proc. Roy. Stat. Soc. 39, 1–38 (1977)zbMATHGoogle Scholar
  5. 5.
    Dice, L.: Measure of the amount of ecological association between species. Ecology 26(3), 29–302 (1945)CrossRefGoogle Scholar
  6. 6.
    Dubrovina-Karni, A., Rosman, G., Kimmel, R.: Multi-region active contours with a single level set function. IEEE Trans. Pattern Anal. Mach. Intell. 37(8), 1585–1601 (2015)CrossRefGoogle Scholar
  7. 7.
    Jung, Y.M., Kang, S.H., Shen, J.: Multiphase image segmentation via modicamortola phase transition. SIAM J. Appl. Math. 67(5), 1213–1232 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Menze, B., Jakab, A., Bauer, S., Kalpathy-Cramer, J., Farahani, K., Kirby, J., et al.: The multimodal brain tumor image segmentation benchmark (BRATS). IEEE Trans. Med. Imaging 34(10), 1993–2024 (2015)CrossRefGoogle Scholar
  9. 9.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577–684 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Pohl, K., Bouix, S., Nakamura, M., Rohlfing, T., McCarley, R., Kikinis, R., Grimson, W., Shenton, M., Wells, W.: A hierarchical algorithm for MR brain image parcellation. IEEE Trans. Med. Imaging 26(9), 1201–1212 (2007)CrossRefGoogle Scholar
  12. 12.
    Pohl, K., Fisher, J., Bouix, S., Shenton, M., McCarley, R., Grimson, W., Kikinis, R., Wells, W.: Using the logarithm of odds to define a vector space on probabilistic atlases. Med. Image Anal. 11(6), 465–477 (2007)CrossRefGoogle Scholar
  13. 13.
    Riklin Raviv, T., Van Leemput, K., Menze, B., Wells, W., Golland, P.: Segmentation of image ensembles via latent atlases. Med. Image Anal. 14(5), 654–665 (2010)CrossRefGoogle Scholar
  14. 14.
    Saye, R., Sethian, J.: The Voronoi implicit interface method for computing multiphase physics. PNAS 108(49), 19498–19503 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Vese, L., Chan, T.: A multiphase level set framework for image segmentation using mumford and shah model. Int. J. Comput. Vis. 50(3), 271–293 (2002)CrossRefzbMATHGoogle Scholar
  16. 16.
    Zhu, S., Yuille, A.: Region competition: unifying snakes, region growing, and bayes/MDL for multiband image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 18(9), 884–900 (1996)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Electrical and Computer Engineering and the Zlotowski Center for NeuroscienceBen-Gurion University of the NegevBeer-ShevaIsrael

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